Snapping to vertex when scaling (Blender 2.8)
The snap scale to vertex tool can be a bit finicky, so here are a bunch of things to try. Basically, any time the vertex you're snapping two doesn't perfectly line up, the snapping is way off.

I don't know your exact set up, but I would be cautious about using Median as the pivot point with a mirror modifier. The Median pivot point doesn't take into the mirror geometry, so you might not be scaling from the right point:



I almost always use the 3D cursor as the pivot point. It can be a little more tedious, but you have much finer control. Select two vertices on opposite sides of the circle and move the 3D cursor to selected.



Then, set your snapping element to 'Active' in the snap settings, and make sure you're targeting the right vertex. You can see below when I initially am snapping to the wrong vertex, it overscales my selection.